Differences between color reproduction devices using additive and subtractive color rendering technologies are well known in the art. Conventional color CRT displays and color television monitors are self-luminous, light-emitting color rendering devices which use an "additive" coloring system. Additive color mixing forms color by adding color stimuli on the retina of the human eye in such a way that they cannot be perceived individually. An additive coloring system may be composed of red, green, and blue (RGB) phosphor signals, referred to as the primary coloring agents (or primary colorants or primary colors) of the system, which combine to form each color of a color image. Such an additive color rendering system is considered to be a linear system because any color producible by the additive system is the sum of the independent primary colorant intensities of the system. The maximum intensity level of all three phosphors produce the system's "white point", that is, the white color of the monitor when the luminance outputs of the three phosphors are at their maximum values. Thus, additive primary colors, when mixed, produce a color of greater intensity than the primary colors themselves. Similarly, the mixture of all three primary colors at the minimal intensity level yields black.
Digital color printers, color copiers, color electrostatic plotters, and similar printing devices are non-self-luminous, light-absorbing and reflective color rendering devices and produce color according to a subtractive color process by applying the primary coloring agents (i.e., the dyes, inks, toners, or pigments) to a white medium (or a transparent medium if back-lit). Light is reflected from the surface on which the color appears and the combination of the light-absorbing coloring agents used "subtract" colors from the source illumination by canceling bands of wavelengths to provide the proper color. In keeping with current practice, colors displayed on a device using a subtractive color system are comprised of certain amounts of cyan, magenta, and yellow (CMY) primary coloring agents (or primary colorants or primary colors); these coloring agent amounts, specified as CMY signals to the device, produce the desired color. Application of no coloring agents produces white, and thus, the device's reference white point, or white color, is usually considered to be the white substrate (paper) on which the primary coloring agents are laid down, with respect to a given source or viewing illuminant. Application of all coloring agents produce black. Alternatively, some subtractive color devices also may use a black coloring agent to darken colors that are not otherwise dark enough as a result of combining the primary coloring agents, or to reduce ink deposition on the substrate, for example in order to achieve better neutral tones. In contrast to the linear additive color reproduction system, the subtractive color reproduction system is nonlinear: mixing coloring agents in the subtractive system results in further spectral absorption, producing a darker color than the primary coloring agents which are mixed. In addition, imperfections in the spectral content of the subtractive primary coloring agents may introduce wavelength reflectance "contamination" of unwanted color when the coloring agents are deposited on a substrate.
All of the colors physically producible by a color reproduction device is called the "gamut" of the device. The gamuts of additive and subtractive color reproduction devices do not correspond to one another because the devices produce color according to the different physical methods described above. Reproducing a color's appearance accurately or appropriately for a particular situation requires selecting the color in the output system's device gamut which most accurately reproduces the appearance of the color as specified in the input system's device gamut.
Accurate and appropriate color reproduction between devices utilizing different color reproduction technology is aided by a device independent representation of color where an input image color is matched to an appropriate output gamut color in a color specification format that is independent of both the input and output primary coloring agent specifications. One such colorimetric, device independent color specification conforms to an internationally recognized and standardized color notation system established by the Commission Internationale de l'Eclairage (the "CIE"). Based on the premises that the spectral reflectance of an object is the percentage of the incident light energy reflected at each wavelength and that the color of an object may be precisely defined as this spectral reflectance, the CIE standard assigns numeric values to colors according to their appearance under standard sources of illumination as viewed by a standard observer, such as the "CIE 1931 Standard Colorimetric Observer" (also known as the "2.degree. Observer", hereafter referred to as the "standard observer"), using three values, X, Y, and Z, to describe colors. The X, Y, and Z values, called the "tristimulus values" of a color, represent a summation of the color contributions of all wavelengths within the spectral distribution of a color sample, corrected for the light source used to illuminate the colored sample and for the color sensitivity of the standard observer. Additional information about the CIE system is available from a number of texts and other sources. In particular, additional relevant information may be found in G. W. Meyer and D. P. Greenberg, "Perceptual Color Spaces for Computer Graphics", in Color and the Computer, H. J. Durrett, ed., Academic Press, 1987, pp. 83-100; and Raster Graphics Handbook, Conrac Corp., Covina, Calif., 1980, at pages A3-1 to A3-37 (hereafter, "Raster Graphics Handbook").
Color correction methods used to map colors from an additive color system's gamut to a subtractive color system's gamut generally use look up tables, matrices, or mathematical transformations for mapping an input image color to its colorimetric color specification and then to an appropriate matching output color, expressed in subtractive primary coloring agent quantities, in the gamut of the subtractive color reproduction device. These methods generally require the measurement of large numbers of colorimetrically measured color patches produced by the subtractive color reproduction device for representing the output color gamut. See, for example, Hung et. al., U.S. Pat. No. 4,959,711, entitled "Method and Apparatus for Correcting the Color of a Printed Image"; and E'Errico, U.S. Pat. No. 4,941,039, entitled "Color Image Reproduction Apparatus Having a Least Squares Look-Up Table Augmented by Smoothing". These techniques, which require matrices or tables which depend on the color of each primary coloring agent, need to be recalculated whenever a primary coloring agent changes.
U.S. Pat. No. 4,751,535, issued to Myers and assigned to Xerox Corporation, the same assignee herein, provides a technique for matching a color which does not require colorimetric measurement of a large number of color patches, and which uses a device independent, linear mixing space, such as a CIE color space, in which to produce an appropriate matching color. A definition of the original color, such as its RGB coordinates, is converted to coordinates in the linear mixing space, such as CIE coordinates. These coordinates, together with coordinates of the toners used by the printer are then used to calculate quantities of toners which will produce a matching color. The calculations match hue, saturation and reflectance so that the matching color appears like the original color and so that characteristics of an original image are preserved.
The complete specification of the color matched printing method of U.S. Pat. No. 4,751,535 may be found in the disclosure thereof which is hereby incorporated by reference. FIG. 1 shows the general steps of the method. Briefly summarized, the method according to U.S. Pat. No. 4,751,535 of determining quantities of the primary coloring agents to be used to generate a matching color begins with the step of colorimetrically measuring, in box 20, the linear mixing coordinates of the three CMY primary coloring agents, the three RGB secondary coloring agents produced by combining the CMY primary coloring agents, black, and the white of the substrate (paper). These measurements include the x, y chromaticity coordinates (or chromaticities) of the CIE color space known as the 1931 Chromaticity Diagram, and the color's luminance, or reflectance value, Y. Next, in box 22, the linear mixing coordinates of the original color are determined through known conversion techniques. The original color's additive RGB coordinates, for example, are converted first into XYZ tristimulus values and then into x, y chromaticities using known matrix transformations and conversion equations. The luminance, or reflectance value Y, of the original color is then adjusted in box 24 for out-of-bounds reflectance values, which occur when an original color is lower in reflectance than the measured black coloring agent or higher in reflectance than the measured paper white.
Then, using the original color's chromaticity coordinates and reflectance value and the linear mixing coordinates of at least three of the primary coloring agents to be applied, the subtractive primary coloring agent quantities needed to reproduce a matching color are determined in boxes 26 through 34. FIG. 2 shows the hexagonally shaped device gamut in which the original color will be matched. The gamut is defined by the two-dimensional x, y chromaticity coordinates of the six primary and secondary measured coloring agents plotted in the 1931 Chromaticity Diagram. The gamut is divided into six mixing triangles by a center point inside the hexagon, each triangle having the center point as one vertex and the end points of one side of the hexagon as its other vertices. An original color falling into one of the mixing triangles will be matched by quantities of the primary and secondary coloring agents at the vertices and a quantity of a neutral or achromatic coloring agent, (either white or black) as shown in FIG. 2.
In box 26, the chromaticities of the center point of the gamut, x.sub.n, y.sub.n, are calculated to be at the coordinates of the achromatic color with the same reflectance, Y.sub.o, as the original color. These achromatic coordinates, x.sub.n, y.sub.n, are calculated using the original color's coordinates, x.sub.o, y.sub.o, and the coordinates of the white, x.sub.w, y.sub.w, and black, x.sub.b, y.sub.b, neutral coloring agents. In the method of U.S. Pat. No. 4,751,535, these center point coordinates are calculated to be on an achromatic mixing line almost perpendicular to the Chromaticity Diagram, the end points of which were determined by the chromaticities of the reference paper white and the black color produced by the device coloring agents. FIG. 3 shows achromatic mixing line 52 bounded by end points B, the x.sub.b, y.sub.b chromaticities at reflectance Y.sub.b, and W, the x.sub.w, y.sub.w chromaticities at reflectance Y.sub.w. Achromatic mixing line 52 is not strictly perpendicular to the x, y mixing plane of the Chromaticity Diagram because the black and white achromatic colors do not have the same chromaticities. The chromaticities x.sub.w, y.sub.w are shown plotted at W', connecting to W along line 54 perpendicular to the Chromaticity Diagram.
As noted above, the matching color lies within one of the mixing triangles of FIG. 2, which is selected next, in box 28 of FIG. 1, based on the coordinates of the center point and of the original color, using a vector cross-product technique and calculation described in detail in U.S. Pat. No. 4,751,535 at col. 12 line 56, and shown diagrammatically in FIG. 8 therein.
The next step, in box 30 (FIG. 1) involves finding the coordinates, x.sub.p, y.sub.p, Y.sub.p, of a "pure hue". As shown in FIG. 4, geometrically and mathematically, a line projecting from the center point x.sub.n, y.sub.n, labeled Neutral in FIG. 3, through the original color intersects a side of the selected mixing triangle. The intersection point x.sub.p, y.sub.p, defines the pure hue, undiluted with neutral coloring agents, which matches the hue of the original color. Calculation of the pure hue permits calculation of the quantities of the two primary and the neutral coloring agents which will approximate the hue, saturation and reflectance of the original color in the device gamut. The primary coloring agents at the end points of the intersected side, labeled Primary1 and Primary2 in FIG. 3, always include one of the CMY primary coloring agents and one of the RGB secondary coloring agents. These coloring agents are "mixed" in relative quantities to obtain the pure hue according to the relationship between the lengths of the parts P1 and P2, into which the line of the intersected side is divided. In particular, the relative quantities of Primary1 and Primary2 have the same ratio as the lengths of the parts P1 and P2 of the linear mixing line bounded by those primaries, as follows: ##EQU1## As used herein, "mixing" refers to the mixing of two or more coloring agents in adjacent areas of a pattern, with negligible superimposition. It will be understood that the dots or other areas of the pattern which contain distinct coloring agents must be small enough to be below the resolution limit of the human eye, so that the pattern is perceived as having a single color.
It is important to note the labeling of line segments P1 and P2 in FIG. 3 to see how the line segments P1 and P2 are proportional to the Primary quantities. When the pure hue at x.sub.p, y.sub.p is equal to Primary1, 100% of Primary1, represented by line segment labeled P1 extending from Primary2, and 0% of Primary2, represented by line segment P2 extending from Primary1, are needed to formulate the pure hue. Similarly, as the pure hue approaches Primary2 along the linear mixing line, the amount of Primary1 decreases from 100% as line segment P1 gets shorter, and the amount of Primary2 increases from 0% as the line segment P2 gets longer.
Thus, the relative quantities of Primary1 and Primary2 can be determined from the P1 and P2 fractions of the total length of the linear mixing line, as follows: ##EQU2## where pure hue coordinates x.sub.p, y.sub.p are first calculated from slope equations for the two intersecting lines.
Finally in box 30 (FIG. 1), in preparation for adjusting saturation and reflectance in box 32, and for finding the primary coloring agent quantities in box 34, the reflectance of the pure color, Y.sub.p, is then calculated using the P1, P2 fractional line lengths and the reflectances of the two primaries, Y.sub.primary1 and Y.sub.primary2 as follows: EQU Y.sub.p =P1Y.sub.primary1 +P2Y.sub.primary2 ( 4)
In box 32 of FIG. 1, a second linear mixing plane is used to adjust the saturation and reflectance of the pure hue in order to obtain the matching color. During this adjustment, the hue, saturation and reflectance is approximated from calculating the relative quantities of the two primary and the neutral primary coloring agents in a manner which preserves the color characteristics of an original image which contains the original color. The adjustment in step 32 may be performed in a number of ways, as appropriate for the specific image being reproduced.
A major consideration in preserving the color characteristics of the original image is how to treat an original color which is outside the three-dimensional gamut of available colors. In general, the relative quantities of the two primaries which generate the pure hue do not need to be adjusted, but the quantities of the neutral coloring agents which are mixed with them must be adjusted to provide a suitable approximation of an original color outside the gamut. Mixing in neutral coloring agents will change the saturation and reflectance of the pure hue but it is usually possible to change these parameters while nonetheless preserving the color characteristics of the original image. For example, if the original image has colors which are distinguishable by saturation differences, the saturation differences can be preserved across a range of available saturation values. Similarly, if the original image has colors distinguishable by reflectance, reflectance differences can be preserved. In general, an appropriate compromise between preserving saturation characteristics and preserving reflectance characteristics can be found. The method of U.S. Pat. No. 4,751,535 permits saturation and reflectance to be flexibly adjusted in whatever way is appropriate to the image being produced.
In the implementation of step 32 described in U.S. Pat. No. 4,751,535, reflectance characteristics of an original image are preserved at the expense of saturation characteristics. FIG. 5 shows a second, triangular mixing plane defined by vertices at the pure hue, at coordinates x.sub.p, y.sub.p, Y.sub.p, at the neutral coloring agent white, at coordinates x.sub.w, y.sub.w, Y.sub.w, and at the neutral coloring agent black, at coordinates x.sub.b, y.sub.b, Y.sub.b. The original color, at coordinates x.sub.o, y.sub.o, Y.sub.o, may either be inside this triangle, if the original color is inside the gamut of the subractive color reproduction device, or outside the triangle, if the original color is outside the gamut of the device. Within the triangular mixing plane, the pure hue, at x.sub.p, y.sub.p, Y.sub.p, is adjusted in all three dimensions from a line of constant reflectance at Y=Y.sub.p to the line of constant reflectance of the original color, Y=Y.sub.o, specifically to a point x.sub.pn, y.sub.pn, Y.sub.o. A reflectance adjustment amount, t.sub.pn, is computed during this adjustment. If the original color falls outside the triangle, the matching color is the most saturated available color on that line, at a point x.sub.pn, y.sub.pn, Y.sub.o, but if the original color is in the triangle, the technique also adjusts the saturation of the matching color to that of the original color, computing a saturation adjustment ratio, R.sub.p/n, during this adjustment. Table 1 summarizes the equations used to complete the adjustments made in box 32 of FIG. 1.
TABLE 1 ______________________________________ Y.sub.neutral = Y.sub.b if Y.sub.o &lt; Y.sub.p (5) Y.sub.neutral = Y.sub.w if Y.sub.o &gt; Y.sub.p (6) ##STR1## (7) x.sub.pn = x.sub.neutral + t.sub.pn (x.sub.p - x.sub.neutral) (8) y.sub.pn = y.sub.neutral + t.sub.pn (y.sub.p - y.sub.neutral) (9) A.sub.o = {(x.sub.o - x.sub.n).sup.2 + (y.sub.o - y.sub.n).sup.2 }.sup.0.5 (10) A.sub.pn = {(x.sub.pn - x.sub.n).sup.2 + (y.sub.pn - y.sub.n).sup.2 }.sup.0.5 (11) ##STR2## (12) ##STR3## (13) ______________________________________
In box 34 of FIG. 1, the quantities of the coloring agents needed to match the original color are determined. Ordinarily in a printer, the white coloring agent is the white of the paper on which the other coloring agents are printed, so that the white coloring agent will be present wherever none of the other coloring agents is printed. Therefore, the only coloring agent quantities to be calculated in box 34 in FIG. 1 are those of the black coloring agent, denoted as a.sub.b, and the two primary coloring agents which mix to provide the pure hue. As shown in equation (17) below, the quantity of black coloring agent can be directly calculated, while the quantities of the primaries must take into account the selection of the primary color pair in box 28. The total amount of the two primary coloring agents which mix is denoted simply as a.sub.p and will differ if the equipment used provides for complete undercover removal by using a black coloring agent, as shown in equations (18) and (19). Table 2 summarizes the equations needed to determine these neutral and primary coloring agents.
TABLE 2 ______________________________________ a.sub.w = the amount of white (14) a.sub.b + a.sub.w + a.sub.p (15).0 Y.sub.0 = a.sub.b Y.sub.b + a.sub.w Y.sub.w + a.sub.p Y.sub.p (16) ##STR4## (17) a.sub.p = R.sub.p/n * t.sub.pn for all Y.sub.0 (undercolor removal) (18) a.sub.p = R.sub.p/n for Y.sub.0 &lt; Y.sub.p (no undercolor removal) (19) ______________________________________
Since the total quantity a.sub.p of the pure hue is made up of two primary coloring agents, a subtractive CMY primary and an adjacent subtractive RGB primary (also called a secondary), the pure hue is actually generated from two of the subtractive CMY primaries. One CMY primary will be present throughout the pure hue areas, while the other CMY primary will be superimposed with the first primary only in the RGB primary areas. The relative amounts of each CMY primary depend in which mixing triangle the original color falls. Table 3 summarizes how to determine the quantities of CMY primaries. P1 and P2 are the quantities determined in equations (2) and (3) above, and the symbol * denotes multiplication.
TABLE 3 ______________________________________ Mixing Triangle Quantity of Quantity of Quantity of Primary1 Primary2 Cyan Magenta Yellow ______________________________________ Cyan Green a.sub.p 0 P2 * a.sub.p Green Yellow P1 * a.sub.p 0 a.sub.p Yellow Red 0 P2 * a.sub.p a.sub.p Red Magenta 0 a.sub.p P1 * a.sub.p Magenta Blue P2 * a.sub.p a.sub.p 0 Blue Cyan a.sub.p P1 * a.sub.p 0 ______________________________________
Finally, in boxes 36 and 38 of FIG. 1, an area coverage pattern is selected which will best approximate the coverage provided by the quantities of the two primary and the neutral coloring agents.
The color matching technique disclosed in U.S. Pat. No. 4,751,535 is easy to use and implement because it is based on the discovery of a computational technique which accurately determines coloring agent quantities directly from the definition of the original color. However, the technique has been found to produce inappropriately matching colors when matching low chroma or nearly achromatic colors. For those colors, unpredictable and undesirable shifts in hue may occur which also may affect the method's ability to produce a balanced and smoothly changing gray scale of achromatic colors. In addition, the printing of standard test patterns of color patches involving uniformly changing colored squares from one CMY primary to another shows the tendency for the method to unpredictably produce under-saturated colors with too much black.
The color matching technique disclosed in U.S. Pat. No. 4,751,535 reproduces accurate colors without the use of extensive colorimetric measurement of sample colors and without extensive sample color remeasurement and recalculation of tables or matrices when coloring agents in the subtractive device change. The method is preferably implemented by measuring and storing in advance the linear mixing coordinates of the subtractive device's coloring agents, provided the variation about the measured values is relatively small, rather than measuring these coordinates each time an image is generated. In practical application, the method has been implemented by supplying in a coded, unchangeable format, the linear mixing coordinates of the colorimetrically measured CMY, RGB, black, and white colors produced by a particular device on a particular substrate under certain manufacturer controlled environmental conditions. The method implemented in this manner produced inaccurately matching colors when a substrate or coloring agent was used in the device which varied from the manufacturer's standards. In such an implementation, there is no ability for the user to tailor the device's color reproduction performance to meet the type of substrate (paper), coloring agent, or environmental condition actually being used.